Spin Displacement Research Articles

Restricted diffusion characteristics in oscillating gradient spin echo with mesoscopic phantom

In diffusion magnetic resonance imaging, oscillating gradient spin echo (OGSE) has an extremely short diffusion time if motion probing gradient (MPG) is applied to the waveform. Further, it can detect microstructural specificity. OGSE changes sensitivity to spin displacement velocity based on the MPG phase. The current study aimed to investigate the restricted diffusion characteristics of each OGSE waveform using the capillary phantom with various b-values, frequencies, and MPG phases. We performed OGSE (b-value = 300, 500, 800, 1200, 1600, and 2000 s/mm2) for the sine and cosine waveforms using the capillary phantom (6, 12, 25, 50, and 100 μm and free water) with a 9.4-T experimental magnetic resonance imaging system and a solenoid coil. We evaluated the axial and radial diffusivity (AD, RD) of each structure size. The output current of the MPG was assessed with an oscilloscope and analyzed with the gradient modulation power spectra by fast Fourier transform.In sine, the sidelobe spectrum was enhanced with increasing frequency, and the central spectrum slightly increased. The difference in RD was detected at 6 and 12 μm; however, it did not depend on the structure scale at 50 or 100 μm and free water. In cosine, the diffusion spectrum was enhanced, whereas the central spectrum decreased with increasing frequency. Both AD and RD in cosine had a frequency dependence, and AD and RD increased with a higher frequency regardless of structure size. AD and RD in either sine or cosine had no evident b-value dependence. We evaluated the OGSE-restricted diffusion characteristics. The measurements obtained diffusion information similar to the pulsed gradient spin echo. Hence, the cosine measurements indicated that a higher frequency could capture faster diffusion within the diffusion phenomena.

Jets and Rings in Images of Spinning Black Holes

We develop a “dual-cone” model for millimeter wavelength emission near a spinning black hole. The model consists of optically thin, luminous cones of emission, centered on the spin axis, which are meant to represent jet walls. The resulting image is dominated by a thin ring. We first consider the effect of the black hole’s spin on the image and show that the dominant effect is to displace the ring perpendicular to the projection of the spin axis on the sky by . This effect is lower order in a * than changes in the shape and size of the photon ring itself but is undetectable without a positional reference. We then show that the centerline of the jet can provide a suitable reference: its location is exactly independent of spin if the observer is outside the cone and nearly independent of spin if the observer is inside the cone. If astrophysical uncertainties can be controlled, then spin displacement is large enough to be detectable by future space very long baseline interferometry missions. Finally, we consider ring substructure in the dual-cone model and show that features in total intensity are not universal and depend on the cone-opening angle.

Asymmetric spin splitting of Laguerre-Gaussian beams in chiral PT-symmetric metamaterials.

We systematically study the spin Hall effect of light (SHEL) in chiral PT-symmetric metamaterials when Laguerre Gaussian beams (LG beams) are incident and discover that cross-polarization (rs p, rp s) and intrinsic orbital angular momentum (IOAM) result in an asymmetric splitting of left-spin circularly polarized (LCP) light and right-spin circularly polarized (RCP) light. Additionally, there are spin Hall shift peaks near |rpp | ≪ |rss | (rs s and rp p are Fresnel reflection coefficients). Altering the topological charge number ℓ, the chiral parameter κ, the dimensionless frequency M, and the incident angle θ may also influence the asymmetric spin splitting and displacement peak. We believe that this research will provide new ways to manipulate and enhance the asymmetric spin splitting of light and provide new applications for spin photonic devices.

Micromorphic modeling of wave propagation in granular materials: Considering particle nonaffine micro-deformation and kinematics decomposition

The objective of this study is to develop a micromorphic model for granular materials and then apply it to investigate the wave propagation. The relationship between particle displacement and rotation is firstly decomposed and thus particle displacement and spin are adopted. The effect of the particle displacement due to particle rotation is also considered. The relative deformation tensors are introduced to describe the local fluctuation of particle kinematics. Based on micro–macro energy conservation, the constitutive relations are consequently derived. The motion equations and boundary conditions can further be obtained building on Hamilton’s principle and subsequently the dispersion equations of plane waves are derived. It is indicated that the present model can reflect sixteen dispersion curves and predict the presence of bandgaps. A further discussion on the dispersion characteristics is made. Finally, the performance of the present model is verified by comparison with existing micromorphic models and other gradient models. • A micromorphic continuum model considering nonaffine micro-deformation is developed. • The interrelation between particle displacement and rotation is decomposed. • The effects of particle spin and particle displacement induced by rotation are considered. • The dispersion relations of plane waves based on micromorphic continua are derived.

DiSpect: Displacement spectrum imaging of flow and tissue perfusion using spin‐labeling and stimulated echoes

We propose a new method, displacement spectrum (DiSpect) imaging, for probing in vivo complex tissue dynamics such as motion, flow, diffusion, and perfusion. Based on stimulated echoes and image phase, our flexible approach enables observations of the spin dynamics over short (milliseconds) to long (seconds) evolution times. The DiSpect method is a Fourier-encoded variant of displacement encoding with stimulated echoes, which encodes bulk displacement of spins that occurs between tagging and imaging in the image phase. However, this method fails to capture partial volume effects as well as blood flow. The DiSpect variant mitigates this by performing multiple scans with increasing displacement-encoding steps. Fourier analysis can then resolve the multidimensional spectrum of displacements that spins exhibit over the mixing time. In addition, repeated imaging following tagging can capture dynamic displacement spectra with increasing mixing times. We demonstrate properties of DiSpect MRI using flow phantom experiments as well as in vivo brain scans. Specifically, the ability of DiSpect to perform retrospective vessel-selective perfusion imaging at multiple mixing times is highlighted. The DiSpect variant is a new tool in the arsenal of MRI techniques for probing complex tissue dynamics. The flexibility and the rich information it provides open the possibility of alternative ways to quantitatively measure numerous complex spin dynamics, such as flow and perfusion within a single exam.

Effect of Fracture on ESR Intensity Using a Low-Velocity Rotary Shear Apparatus

Abstract We sheared simulated-quartz gouges using a low-velocity rotary shear apparatus and evaluated the relationship between electron spin resonance (ESR) intensity and displacement quantitatively considering problems of contaminants. ESR intensity of E1’ centre increased while OHC and peroxy centre kept constant with the increasing displacement up to 1.4 m. Microstructural analysis showed grain size reduction and fracture of starting gouges; hence, the fracture can affect the change in ESR intensity. ESR measurements were also conducted for starting gouges with variable amounts of contaminants, and it was confirmed that the effect of contaminants on the change in ESR intensity was negligible. Moreover, we estimated the temperature rise by the frictional heating on the surface and between particles, and it was shown that the effect of frictional heating on ESR intensity was also negligible in our experimental condition. Therefore, we could clarify the relationship between ESR intensity and fracturing with various displacements separately from contaminants and frictional heating. The results imply that the zero-setting of ESR signals cannot occur by the fracture with low frictional heating at the shallow depth.

Unipolar MR elastography: Theory, numerical analysis and implementation.

In MR elastography (MRE), zeroth moment balanced motion‐encoding gradients (MEGs) are incorporated into MRI sequences to induce a phase shift proportional to the local displacement caused by external actuation. To maximize the signal‐to‐noise ratio (SNR), fractional encoding is employed, i.e., the MEG duration is reduced below the wave period. Here, gradients encode primarily the velocity of the motion‐reducing encoding efficiency. Thus, in GRE‐MRE, T2* decay and motion sensitivity have to be balanced, imposing a lower limit on repetition times (TRs).We propose to use a single trapezoidal gradient, a “unipolar gradient”, to directly encode spin displacement. Such gradients cannot be used in conventional sequences as they exhibit a large zeroth moment and dephase magnetization. By time‐reversing a spoiled SSFP sequence, the spoiling gradient becomes an efficient unipolar MEG. The proposed “unipolar MRE” technique benefits from this approach in three ways: first, displacement encoding is split over multiple TRs increasing motion sensitivity; second, spoiler and MEG coincide, allowing a reduction in TR; third, motion sensitivity of a typical unipolar lobe is of an order of magnitude higher than a bipolar MEG of equal duration.In this work, motion encoding using unipolar MRE is analyzed using the extended phase graph (EPG) formalism with a periodic motion propagator. As an approximation, the two‐transverse TR approximation for diffusion‐weighted SSFP is extended to incorporate cyclic motion. A complex encoding efficiency metric is introduced to compare the displacement fields of unipolar and conventional GRE‐MRE sequences in both magnitude and phase. The derived theoretical encoding equations are used to characterize the proposed sequence using an extensive parameter study. Unipolar MRE is validated against conventional GRE‐MRE in a phantom study showing excellent agreement between measured displacement fields. In addition, unipolar MRE yields significantly increased octahedral shear strain‐SNR relative to conventional GRE‐MRE and allows for the recovery of high stiffness inclusions, where conventional GRE‐MRE fails.

Comparison of two-compartment exchange and continuum models of dMRI in skeletal muscle

Clinical diffusion MRI (dMRI) is sensitive to micrometer scale spin displacements, but the image resolution is ∼mm, so the biophysical interpretation of the signal relies on establishing appropriate subvoxel tissue models. A class of two-compartment exchange models originally proposed by Kärger have been used successfully in neural tissue dMRI. Their use to interpret the signal in skeletal muscle dMRI is challenging because myocyte diameters are comparable to the root-mean-square of spin displacement and their membrane permeability is high. A continuum tissue model consisting of the Bloch–Torrey equation integrated by a hybrid lattice Boltzmann scheme is used for comparison. The validity domain of a classical two-compartment tissue model is probed by comparing it with the prediction of the continuum model for a 2D unidirectional composite continuum model of myocytes embedded in a uniform matrix. This domain is described in terms of two dimensionless parameters inspired by mass transfer phenomena, the Fourier (F) and Biot (B) numbers. The two-compartment model is valid when and , or when and . The model becomes less appropriate for muscle dMRI as the cell diameter and volume fraction increase, with the primary source of error associated with modeling diffusion in the extracellular matrix.

Conserved spin current for the Mott relation

The conserved bulk spin current [Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], defined as the time derivative of the spin displacement operator, ensures automatically the Onsager relation between the spin Hall effect (SHE) and the inverse SHE. Here, we reveal another desirable property of this conserved spin current: the Mott relation linking the SHE and its thermal counterpart, the spin Nernst effect (SNE). According to the Mott relation, the SNE is known once the SHE is understood. In a two-dimensional Dirac-Rashba system with a smooth scalar disorder potential, we find a sign change of the spin Nernst conductivity when tuning the chemical potential.

Clinical feasibility of using mean apparent propagator (MAP) MRI to characterize brain tissue microstructure

Diffusion tensor imaging (DTI) is the most widely used method for characterizing noninvasively structural and architectural features of brain tissues. However, the assumption of a Gaussian spin displacement distribution intrinsic to DTI weakens its ability to describe intricate tissue microanatomy. Consequently, the biological interpretation of microstructural parameters, such as fractional anisotropy or mean diffusivity, is often equivocal. We evaluate the clinical feasibility of assessing brain tissue microstructure with mean apparent propagator (MAP) MRI, a powerful analytical framework that efficiently measures the probability density function (PDF) of spin displacements and quantifies useful metrics of this PDF indicative of diffusion in complex microstructure (e.g., restrictions, multiple compartments). Rotation invariant and scalar parameters computed from the MAP show consistent variation across neuroanatomical brain regions and increased ability to differentiate tissues with distinct structural and architectural features compared with DTI-derived parameters. The return-to-origin probability (RTOP) appears to reflect cellularity and restrictions better than MD, while the non-Gaussianity (NG) measures diffusion heterogeneity by comprehensively quantifying the deviation between the spin displacement PDF and its Gaussian approximation. Both RTOP and NG can be decomposed in the local anatomical frame for reference determined by the orientation of the diffusion tensor and reveal additional information complementary to DTI. The propagator anisotropy (PA) shows high tissue contrast even in deep brain nuclei and cortical gray matter and is more uniform in white matter than the FA, which drops significantly in regions containing crossing fibers. Orientational profiles of the propagator computed analytically from the MAP MRI series coefficients allow separation of different fiber populations in regions of crossing white matter pathways, which in turn improves our ability to perform whole-brain fiber tractography. Reconstructions from subsampled data sets suggest that MAP MRI parameters can be computed from a relatively small number of DWIs acquired with high b-value and good signal-to-noise ratio in clinically achievable scan durations of less than 10min. The neuroanatomical consistency across healthy subjects and reproducibility in test–retest experiments of MAP MRI microstructural parameters further substantiate the robustness and clinical feasibility of this technique. The MAP MRI metrics could potentially provide more sensitive clinical biomarkers with increased pathophysiological specificity compared to microstructural measures derived using conventional diffusion MRI techniques.

Magnetic domain-wall motion twisted by nanoscale probe-induced spin transfer

A method for deterministic control of magnetism using an electrical stimulus is highly desired for the new generation of magnetoelectronic devices. Much effort has been focused on magnetic domain-wall (DW) motion manipulated by a successive injection of spin-polarized current into a magnetic nanostructure. However, an integrant high-threshold current density of ${10}^{11}\ensuremath{\sim}{10}^{12}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/{\mathrm{m}}^{2}$ inhibits the integration with low-energy-cost technology. Here, we report an approach to manipulate a single magnetic domain wall with a perpendicular anisotropy in a manganite/dielectric/metal capacitor using a probe-induced spin displacement. A spin-transfer torque (STT) occurs in the strongly correlated manganite film during the spin injection into the capacitor from the nanoscale magnetized tip with an ultralow voltage of 0.1 V, where a lower bound of the estimated threshold spin-polarized current density is $\ensuremath{\sim}{10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{A}/{\mathrm{m}}^{2}$ at the tip/manganite interface. The dynamic of DW motions are analyzed using the Landau-Lifshitz-Gilbert method. This probe-voltage-controlled DW motion, at an ambient condition, demonstrates a critical framework for the fundamental understanding of the manipulation of the nanomagnet systems with low-energy consumption.

Influence of horizontal static magnetic field on the stability of electromagnetic levitated Cu molten droplet

For an electromagnetically levitated (EML) molten droplet, there usually exist some unstable factors, such as internal fluid convection, quick spin and horizontal displacement and so on. As a result, stabilizing the droplet is very important for EML technology. In this paper, a horizontal static magnetic field is imposed on an EML Cu droplet through a U-shaped static magnetic component. The shape oscillation of a Cu droplet is recorded continuously under different magnetic field intensities using a high speed camera. The effects of static magnetic field on the oscillation frequency, amplitude and spin angle of the droplet are analyzed from the recorded data of droplet shape. The result shows that when the strength of the static magnetic field exceeds 0.3 T the solid Cu is levitated statically without any spin and horizontal movement. For molten Cu droplet, its amplitudes of the R-, A and Dmax are reduced by 25%, 76% and 60% respectively when a static magnetic field with 0.15 T is imposed. With the increase of magnetic field strength the amplitude and frequency of oscillation decease continuously. However, when the intensity of the static magnetic field is 0.3 T, its frequency is 1 Hz higher than that when the intensity of the static magnetic field is 0.2 T. Finally, the result indicates that the horizontal static magnetic field can inhibit the spin of the levitated droplets. For instance, when the strength of the magnetic field is 0.53 T the droplet spins are within a very narrow angle of 10°, which is quite smaller than in the case without static magnetic field. These results exhibit that the imposed horizontal static magnetic field can effectively improve the stability of electromagnetic levitated droplet.

Properties of the low-spin high-spin interface during the relaxation of spin-crossover materials, investigated through an electro-elastic model

The present work is devoted to the spatio-temporal investigations of spin-crossover lattices during their thermal relaxation from high- to low-spin state. The analysis is performed using Monte Carlo simulations on a distortable 2D lattice the sites of which are occupied by high-spin (HS) or low-spin (LS) atoms. The lattice is circular in shape and the HS to LS transformation results in single domain nucleation followed by growth and propagation processes. The evolution of the LS:HS interface is monitored during the relaxation process, through the mapping of spin states, displacement fields, local stresses, and elastic energy. The results show a curved interface, the curvature of which is reversed at the mid-transformation. The local stresses and elastic energy peak at the vicinity of the HS:LS interface, with sizeable dependence upon the position along the front line which evidences the edge effects.

Spin displacements of a Gaussian beam at an air–multilayer-film interface

We theoretically and experimentally study the unique spin displacements of a linearly polarized Gaussian beam reflected from an air--multilayer-film interface with effective complex reflection coefficients. It is found that the left- and right-handed spin components exhibit distinct intensity distributions and manifest unequal values of displacements. Furthermore, the displacements are very sensitive to the layers' thickness. This provides an efficient pathway for controlling the spin displacements of light, such as enhancement of spin displacements to microns at specific incident angles. The experimental results with $P$- and $S$-polarized light are in good agreement with the theoretical predictions.

Nonnegative Diffusion Orientation Distribution Function

Because of the well-known limitations of diffusion tensor imaging (DTI) in regions of low anisotropy and multiple fiber crossing, high angular resolution diffusion imaging (HARDI) and Q-Ball Imaging (QBI) are used to estimate the probability density function (PDF) of the average spin displacement of water molecules. In particular, QBI is used to obtain the diffusion orientation distribution function (ODF) of these multiple fiber crossing. As a probability distribution function, the orientation distribution function should be nonnegative which is not guaranteed in the existing methods. This paper proposes a novel technique to guarantee the nonnegative property of ODF by solving a convex optimization problem, which has a convex quadratic objective function and a constraint involving the nonnegativity requirement on the smallest Z-eigenvalue of the diffusivity tensor. Using convex analysis and optimization techniques, we first derive the optimality conditions of this convex optimization problem. Then, we propose a gradient descent algorithm to solve this problem. We also present formulas for determining the principal directions (maxima) of the ODF. Numerical examples on synthetic data as well as MRI data are displayed to demonstrate the significance of our approach.

Perturbation Analysis of Relationship of Conebeam CT and Stereoscopic Optical Localization System in Frameless Stereotactic Radiosurgery

Purpose/Objective(s): Treatment targets under frameless stereotactic radiosurgery (SRS) can be localized by optical guidance platform (OGP) using a stereoscopic camera. The registration of the target to isocenter is by IR markers on a patient bite block. The rigidity of the bite block and treatment target will determine the accuracy of the treatment. However, the offset between the biteblock and target cannot be visually detected; therefore conebeam CT(CBCT) is used to verify the accuracy of target localization based on information of anatomy volume. In this study, the relationship between these two localization methods was investigated by sequential perturbations of the setup.

The effect of finite diffusion gradient pulse duration on fibre orientation estimation in diffusion MRI

An essential step for fibre-tracking is the accurate estimation of neuronal fibre orientations within each imaging voxel, and a number of methods have been proposed to reconstruct the orientation distribution function based on sampling three-dimensional q-space. In the q-space formalism, very short (infinitesimal) gradient pulses are the basic requirement to obtain the true spin displacement probability density function. On current clinical MR systems however, the diffusion gradient pulse duration (δ) is inevitably finite due to the limit on the achievable gradient intensity. The failure to satisfy the short gradient pulse (SGP) requirement has been a recurrent criticism for fibre orientation estimation based on the q-space approach. In this study, the influence of a finite δ on the DW signal measured as a function of gradient direction is described theoretically and demonstrated through simulations and experimental models. Our results suggest that the current practice of using long δ for DW imaging on human clinical MR scanners, which is enforced by hardware limitations, might in fact be beneficial for estimating fibre orientations. For a given b-value, the prolongation of δ is advantageous for estimating fibre orientations for two reasons: first, it leads to a boost in DW signal in the transverse plane of the fibre. Second, it stretches out the shape of the measured diffusion profile, which improves the contrast between DW orientations. This is especially beneficial for resolving crossing fibres, as this contrast is essential to discriminate between different fibre directions.

Magnetoelectric coupling induced by exchange striction in frustrated Ising spin chain: Monte Carlo simulation

The fascinating magnetoelectric behavior as observed in Ca3CoMnO6 compound [Choi et al., Phys. Rev. Lett. 100, 047601 (2008)] is investigated by using Monte Carlo simulation based on a one-dimensional elastic Ising model. The macroscopic polarization results from the ionic displacements attributed to the exchange striction in an up-up-down-down (↑↑↓↓) spin ordering. In this scenario, the microscopic structures of spin and ionic displacement are investigated at different temperatures under different external electric fields to illuminate in detail the microscopic mechanism of the strong coupling between the magnetism and the ferroelectricity. It is revealed that the change in spin configuration dependent on temperature induces the freezing and melting phenomena of the polarized domains and thus the complicated temperature-dependent ferroelectric behavior in the whole low temperature range, namely the decline of the macroscopic polarization and the broad peak of dielectric constant. On the other hand, an external electric field also has influence on the magnetic structure through affecting the ionic displacements.

THE COMPETITIVE REACTION MECHANISM IN EXOTIC NUCLEAR REACTIONS

Two principal reaction dynamics are introduced. One is the spin displacement, which is caused from the spin-dependence of the interaction, and the other is the isovector displacement, which is caused from the isospin-dependence of it. The competition of these two dynamics is a rather important factor as the target or projectile has more excess neutrons or protons. In this paper the competitive reaction mechanism is theoretically formulated, where the time-dependent mean field calculations are performed for justification.

Sensitivity of diffusion weighted steady state free precession to anisotropic diffusion

Diffusion-weighted steady-state free precession (DW-SSFP) accumulates signal from multiple echoes over several TRs yielding a strong sensitivity to diffusion with short gradient durations and imaging times. Although the DW-SSFP signal is well characterized for isotropic, Gaussian diffusion, it is unclear how the DW-SSFP signal propagates in inhomogeneous media such as brain tissue. This article presents a more general analytical expression for the DW-SSFP signal which accommodates Gaussian and non-Gaussian spin displacement probability density functions. This new framework for calculating the DW-SSFP signal is used to investigate signal behavior for a single fiber, crossing fibers, and reflective barriers. DW-SSFP measurements in the corpus callosum of a fixed brain are shown to be in good agreement with theoretical predictions. Further measurements in fixed brain tissue also demonstrate that 3D DW-SSFP out-performs 3D diffusion weighted spin echo in both SNR and CNR efficiency providing a compelling example of its potential to be used for high resolution diffusion tensor imaging.